## Τρίτη, 17 Οκτωβρίου 2017

### 2005 IMO Shortlist G7

In an acute triangle $ABC$, let $D, E, F , P , Q, R$ be the feet of perpendiculars from $A, B, C, A, B, C$  to $BC, CA, AB, EF , F D, DE$, respectively. Prove that $p(ABC)p(P QR) \ge p(DEF)^2$, where $p(T)$ denotes the perimeter of the triangle $T$ .

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